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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Feedback control systems01:26

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model01:13

Parameters Affecting Nonlinear Elimination: Zero-Order Input, First-Order Absorption and Two-Compartment Model

Drugs administered through various routes can lead to nonlinear elimination, resulting in complex pharmacokinetic behaviors crucial to understanding efficacious drug dosing.
When a drug is administered through a constant intravenous infusion and eliminated via nonlinear pharmacokinetics, it follows zero-order input. For example, oral drugs undergo first-order absorption upon administration and are eliminated through nonlinear pharmacokinetics.
In the case of subcutaneously administered drugs,...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

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Related Experiment Video

Updated: Jul 2, 2026

Functional Imaging of Auditory Cortex in Adult Cats using High-field fMRI
10:50

Functional Imaging of Auditory Cortex in Adult Cats using High-field fMRI

Published on: February 19, 2014

Acoustic FMRI noise: linear time-invariant system model.

Carlos V Rizzo Sierra1, Maarten J Versluis, Johannes M Hoogduin

  • 1Department of Biomedical Engineering, Faculty of Mathematics and Natural Sciences, University of Groningen, NL 9747 AG Groningen, The Netherlands. c.rizzo@med.umcg.nl

IEEE Transactions on Bio-Medical Engineering
|August 21, 2008
PubMed
Summary

Functional magnetic resonance imaging (fMRI) acoustic noise interferes with auditory studies. This study models MR scanner noise, predicting sound pressure levels for echo planar imaging sequences, aiding noise reduction efforts.

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Area of Science:

  • Medical Imaging
  • Acoustics
  • Neuroscience

Background:

  • Functional magnetic resonance imaging (fMRI) is crucial for localizing brain activation.
  • Scanner-generated acoustic noise poses a significant challenge for auditory fMRI studies.
  • Understanding and modeling this noise is essential for developing reduction strategies.

Purpose of the Study:

  • To model the acoustic noise produced by an MR scanner as a linear electroacoustical system.
  • To determine the transfer function of an MR scanner using different input specifications.
  • To validate the model's predictive capabilities by comparing calculated and measured acoustic outputs for EPI sequences.

Main Methods:

  • Modeled the MR scanner as a linear electroacoustical system relating gradient currents to sound pressure.
  • Determined the scanner's transfer function using scanner software calculations and direct gradient current recordings.
  • Analyzed impulse response to ascertain gradient coil system properties.
  • Calculated and measured the acoustic output for echo planar imaging (EPI) sequences.

Main Results:

  • The transfer function determined using scanner software calculations is reliable up to 4 kHz compared to direct gradient current measurements.
  • The model accurately predicted the sound pressure level (SPL) for EPI sequences (104 dB predicted vs. 102 dB measured).
  • Predicted and measured EPI pressure waveforms showed similarities and some differences.

Conclusions:

  • Modeling MR scanner acoustic noise using linear electroacoustical principles is feasible and useful.
  • Scanner software-derived gradient waveforms offer a reliable method for transfer function determination when direct measurements are unavailable.
  • The validated model provides a foundation for understanding and mitigating acoustic noise in fMRI, particularly for auditory research.